SOLUTION: Please help me solve for n. {{{(32/11)(11^(2n))+(11^(2n-1))=3}}} The correct answer given for this is n=0. I totally have no idea on how to solve this and I don't think my wor

Algebra ->  Exponents -> SOLUTION: Please help me solve for n. {{{(32/11)(11^(2n))+(11^(2n-1))=3}}} The correct answer given for this is n=0. I totally have no idea on how to solve this and I don't think my wor      Log On


   

Question 953583: Please help me solve for n.
%2832%2F11%29%2811%5E%282n%29%29%2B%2811%5E%282n-1%29%29=3
The correct answer given for this is n=0.
I totally have no idea on how to solve this and I don't think my workings are even close to the solution but here they are:
%2832%2F11%29%2811%5E%282n%29%29%2B%2811%5E%282n%29%29%2811%5E-1%29=3
%2832%2F11%29%28%2811%5E2%29%2B%2811%5E2%29%29%5En%2A%2811%5E-1%29=3
%2832%2F11%29%28242%5En%29%2811%5E-1%29=3
I didn't know what to do next after that line so I stopped there.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Reverse of Distributive Property.

%2832%2F11%29%2811%5E%282n-1%29%29%2811%5E%28-1%29%2B1%29=3

Another step could be preparation for simplification,
32%281%2F11%29%2811%5E%282n-1%29%29%2811%5E%28-1%29%2B1%29=3

32%2811%5E%282n-1%29%29%2811%5E%28-1%29%29%2811%5E%28-1%29%2B1%29=3

continue this simplification
32%2811%5E%282n-1%29%29%281%2F121%2B1%2F11%29=3

You want to isolate the exponential factor.
%2811%5E%282n-1%29%29%281%2F121%2B11%2F121%29=3%2F32, which is a combined step...

%2811%5E%282n-1%29%29%2812%2F121%29=3%2F32

...enough to understand; you still want to isolate the exponential factor; and you can finish...